Home button does not work when the phone is locked

If you replaced the screen, maybe it is defective or a cable is not seated correctly. You may also need to clear your fingerprint scans and re-enter them. I haven't tried replacing the screen on my 5S, so I am just guessing. I would try the settings before opening the phone up again. See if the fingerprint home button even works as a fingerprint reader. The home button only unlocks the screen if your fingerprint reads first.

I had this exact same problem. Although my touch id didnt work either. When i changed my screen i had to move the back shield metal plate from my phone to the new screen. That back metal shield plate has the home button connector on it. I believed i damaged the home button connector when I disconnected the home button from my old screen, i can see the connector was now quite loose when i touched it. I decided to change the metal shield plate (you can buy it of ebay for like $10-$15). Once changed my home button now works fine. It also fixed my touch id which I wasn't expecting. Bonus!

I know this is an old post but i hope it helps someone else.

I had this exact same problem. Although my touch id didnt work either. When i changed my screen i had to move the back shield metal plate from my phone to the new screen. That back metal shield plate has the home button connector on it. I believed i damaged the home button connector when I disconnected the home button from my old screen, i can see the connector was now quite loose when i touched it. I decided to change the metal shield plate (you can buy it of ebay for like $10-$15). Once changed my home button now works fine. It also fixed my touch id which I wasn't expecting. Bonus!